Given $ m \angle ABC = 5x + 89$, and $ m \angle CBD = 2x - 7$, find $m\angle ABC$. $B$ $A$ $D$ $C$
From the diagram, we see that together ${\angle ABC}$ and ${\angle CBD}$ form ${\angle ABD}$ , so $ {m\angle ABC} + {m\angle CBD} = {m\angle ABD}$ Since $\angle ABD$ is a straight angle, we know ${m\angle ABD = 180}$ Substitute in the expressions that were given for each measure: $ {5x + 89} + {2x - 7} = {180}$ Combine like terms: $ 7x + 82 = 180$ Subtract $82$ from both sides: $ 7x = 98$ Divide both sides by $7$ to find $x$ $ x = 14$ Substitute $14$ for $x$ in the expression that was given for $m\angle ABC$ $ m\angle ABC = 5({14}) + 89$ Simplify: $ {m\angle ABC = 70 + 89}$ So ${m\angle ABC = 159}$.